Topological Quantum Computation from non-abelian ... - Paul Fendley

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A quantum computer is massively parallel: the initial state can be a superposition of everyphone number in the Manhattan phone book.A single unitary transformation acts on all of these at once: could do reverse lookups inorder√N time as opposed to order N .Numbers could be prime-factored in polynomial time.But with every silver lining.... . .6
Errors!In a classical computer, just be redundant.In a quantum computer, errors are continuous, not just bit flips. Moreover, measurementdestroys the superposition. How do we know errors have occurred?!? Need to preserve+αIt’s <strong>non</strong>-trivial to show that error correction is even possible for quantum computers.7
Page 1 and 2: Topological Quantum Computationfrom
Page 3: Outline:1. What are non-abelian sta
Page 9: In three dimensions, the only stati
Page 12 and 13: Even more spectacular phenomena tha
Page 14 and 15: We need to understand fusion: what
Page 16 and 17: φ × φ = I + φPrecise meaning in
Page 18 and 19: To make a qubit requires 4 Fibonacc
Page 20 and 21: One can find the braiding and fusin
Page 22 and 23: A simple way of satisfying the cons
Page 24 and 25: These relations can all be treated
Page 26 and 27: The problem: find a quantum Hamilto
Page 28 and 29: The leading candidate wavefunction
Page 30 and 31: A (hopefully not unique) procedure
Page 32 and 33: The excitations with non-abelian br
Page 34 and 35: These nets can be described using t
Page 36 and 37: Such loops satisfy a property under
Page 38 and 39: We find models with deconfined Fibo
Page 40 and 41: This allows construction of a quant
Page 42 and 43: 2. Level-rank duality: Here we expl

Topological Quantum Computation from non-abelian ... - Paul Fendley

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